In the present work, the capacity of phase field method to highlight microstructural changes during the spinodal decomposition of a given binary alloy basing on the Cahn-Hilliard equation is presented. Then, growth and coarsening of precipitates are studied using the KKS (Kim-Kim-Suzuki) model, which includes Cahn-Hilliard and Allen-Cahn equations. The implementation of time stepping algorithms to resolve Phase-Field equations is illustrated. Within Fourier space, using semi-implicit spectral method, it has been demonstrated that it allows faster computing than schemes based on finite difference method. First, spinodal decomposition of a given binary alloy under isothermal loading is implemented and three time stepping approaches are applied: constant time stepping, non- iterative and an iterative method. While the non-iterative method is faster than the constant time stepping scheme, the iterative one, although relatively more CPU consuming, can guarantee the convergence of the computing. These methods are combined in an innovative approach tested on 1D, 2D and 3D grids. The effectiveness of the adopted adaptive time-stepping algorithm allows resolving equations in reasonable CPU time. It predicts different physical phenomena, such as phase separation and growth and coarsening of precipitates induced by important interfacial energies
